Levi Streeter - Finding Records of Civil War Service

In all my years of researching my fourth-great-grandfather Levi Streeter, I'd never come across anything regarding him serving in the Civil War until this past Sunday, when I noticed that a new memorial stone had been built for him at the cemetery. The stone and the serviceman marker next to it both indicate that he was a Union Volunteer.

I've been digging around various resources and can't find any mention of him serving. He would have been nearly 60 at the start of the war, so it seems highly improbable. It doesn't seem like he could have been confused with another Levi because the only other Levi Franklin "Frank" Streeter in the family was my Levi's grandson, born in 1871. Is this just a misleading marker?

So far, I've tried Fold3, CWSS, NPS, and the few New Hampshire (incomplete) indices I could find. The only Levi Streeter who keeps coming up is one in Iowa. Where else should I be looking to rule this information in or out?